Impulsive delayed reward discounting (DRD) is an important behavioral process in alcohol use disorders (AUDs), reflecting incapacity to delay gratification. Recent work in neuroeconomics has begun to unravel the neural mechanisms supporting DRD, but applications of neuroeconomics in relation to AUDs have been limited. This study examined the neural mechanisms of DRD preferences in AUDs, with emphasis on dissociating activation patterns based on DRD choice type and level of cognitive conflict. Heavy drinking adult men with (n = 13) and without (n = 12) a diagnosis of an AUD completed a monetary DRD task during a functional magnetic resonance imaging scan. Participant responses were coded based on choice type (impulsive versus restrained) and level of cognitive conflict (easy versus hard). AUD+ participants exhibited significantly more impulsive DRD decision-making. Significant activation during DRD was found in several decision-making regions, including dorsolateral prefrontal cortex (DLPFC), insula, posterior parietal cortex (PPC), and posterior cingulate. An axis of cognitive conflict was also observed, with hard choices associated with anterior cingulate cortex and easy choices associated with activation in supplementary motor area. AUD+ individuals exhibited significant hyperactivity in regions associated with cognitive control (DLPFC) and prospective thought (PPC) and exhibited less task-related deactivation of areas associated with the brain's default network during DRD decisions. This study provides further clarification of the brain systems supporting DRD in general and in relation to AUDs.